Our biggest limitation in terms of implementation is scale, as we have only evaluated relatively simple toy distributions with a custom non-optimized implementation of HMC. A thorough comparison of our proposed family of methods with existing inference methods on larger problems will be an important next step. One interesting avenue to scale up our framework will be to combine insights from stochastic-gradient VI methods [1]}, with MCMC methods that make use of stochastic gradients of \(\log {\rm p}\)  [2]}, [3]}, i.e. making use of stochastic values of \(\nabla {\rm KL}({\rm q}||{\rm p})\)  in (REF ).
